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Dobson unit-Derivation-A Dobson unit is the total amount of a trace gas per unit area. In atmospheric sciences, this is referred to as a column density. How, though, do we go from units of molecules per cubic meter, a volume, to molecules per square centimeter, an area? This must be done by integration. To get a column... | milkshake721/2.1M-wiki-STEM |
Dobson unit-Derivation-And thus we come up with the value of 1 DU, which is 2.69×1020 molecules per meter squared. | milkshake721/2.1M-wiki-STEM |
Indigenous bundle-Indigenous bundle-In mathematics, an indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced by Robert C. Gunning (1967). Indigenous bundles for curves over p-adic fields were introduced by Shin... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Jordan matrix-In the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities are the zero 0 and one 1), where each block along the diagonal, called a Jordan block, has the following form: | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Definition-Every Jordan block is specified by its dimension n and its eigenvalue λ∈R , and is denoted as Jλ,n. It is an n×n matrix of zeroes everywhere except for the diagonal, which is filled with λ and for the superdiagonal, which is composed of ones.
Any block diagonal matrix whose blocks are Jordan... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Linear algebra-Any n × n square matrix A whose elements are in an algebraically closed field K is similar to a Jordan matrix J, also in Mn(K) , which is unique up to a permutation of its diagonal blocks themselves. J is called the Jordan normal form of A and corresponds to a generalization of the diagona... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Linear algebra-The same goes for all the matrices A similar to J, so idx Aλ can be defined accordingly with respect to the Jordan normal form of A for any of its eigenvalues spec A . In this case one can check that the index of λ for A is equal to its multiplicity as a root of the minimal polynomial ... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Linear algebra-Note that knowing a matrix's spectrum with all of its algebraic/geometric multiplicities and indexes does not always allow for the computation of its Jordan normal form (this may be a sufficient condition only for spectrally simple, usually low-dimensional matrices): the Jordan decompositio... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Functions of matrices-Let A∈Mn(C) (that is, a n × n complex matrix) and C∈GLn(C) be the change of basis matrix to the Jordan normal form of A; that is, A = C−1JC. Now let f (z) be a holomorphic function on an open set Ω such that specA⊂Ω⊆C ; that is, the spectrum of the matrix is contained inside the ... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Functions of matrices-The Jordan normal form allows the computation of functions of matrices without explicitly computing an infinite series, which is one of the main achievements of Jordan matrices. Using the facts that the kth power ( k∈N0 ) of a diagonal block matrix is the diagonal block matrix whose ... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Dynamical systems-Now suppose a (complex) dynamical system is simply defined by the equation where z:R+→R is the (n-dimensional) curve parametrization of an orbit on the Riemann surface R of the dynamical system, whereas A(c) is an n × n complex matrix whose elements are complex functions of a d-dimensi... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Dynamical systems-From the tangent space dynamics, this means that the orthogonal decomposition of the dynamical system's phase space changes and, for example, different orbits gain periodicity, or lose it, or shift from a certain kind of periodicity to another (such as period-doubling, cfr. logistic map)... | milkshake721/2.1M-wiki-STEM |
Jordan matrix-Linear ordinary differential equations-The simplest example of a dynamical system is a system of linear, constant-coefficient, ordinary differential equations; that is, let A∈Mn(C) and z0∈Cn whose direct closed-form solution involves computation of the matrix exponential: Another way, provided the solut... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Undertow (water waves)-In physical oceanography, undertow is the undercurrent that moves offshore while waves approach the shore. Undertow is a natural and universal feature for almost any large body of water; it is a return flow compensating for the onshore-directed average transport of water by... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Oceanography-An "undertow" is a steady, offshore-directed compensation flow, which occurs below waves near the shore. Physically, nearshore, the wave-induced mass flux between wave crest and trough is onshore directed. This mass transport is localized in the upper part of the water column, i.e. a... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Oceanography-Seaward mass flux An exact relation for the mass flux of a nonlinear periodic wave on an inviscid fluid layer was established by Levi-Civita in 1924. In a frame of reference according to Stokes' first definition of wave celerity, the mass flux Mw of the wave is related to the wave's... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Oceanography-Similarly, Longuet Higgins showed in 1975 that – for the common situation of zero mass flux towards the shore (i.e. Stokes' second definition of wave celerity) – normal-incident periodic waves produce a depth- and time-averaged undertow velocity: u¯=−2Ekρch, with h the mean water de... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Oceanography-For small-amplitude waves, there is equipartition of kinetic ( Ek ) and potential energy ( Ep ): Ew=Ek+Ep≈2Ek≈2Ep, with Ew the total energy density of the wave, integrated over depth and averaged over horizontal space. Since in general the potential energy Ep is much easier to meas... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Oceanography-For irregular waves the required wave height is the root-mean-square wave height rms ≈8σ, with σ the standard deviation of the free-surface elevation.
The potential energy is Ep=12ρgσ2 and Ew≈ρgσ2.
The distribution of the undertow velocity over the water depth is a topic of ongoi... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Confusion with rip currents-In contrast to undertow, rip currents are responsible for the great majority of drownings close to beaches. When a swimmer enters a rip current, it starts to carry them offshore. The swimmer can exit the rip current by swimming at right angles to the flow, parallel to ... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Confusion with rip currents-On the United States Lifesaving Association website, it is noted that some uses of the word "undertow" are incorrect: A rip current is a horizontal current. Rip currents do not pull people under the water—they pull people away from shore. Drowning deaths occur when peo... | milkshake721/2.1M-wiki-STEM |
Undertow (water waves)-Confusion with rip currents-In some regions, rip currents are referred to by other, incorrect terms such as "rip tides" and "undertow". We encourage exclusive use of the correct term—rip currents. Use of other terms may confuse people and negatively impact public education efforts. | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Voice (phonetics)-Voice or voicing is a term used in phonetics and phonology to characterize speech sounds (usually consonants). Speech sounds can be described as either voiceless (otherwise known as unvoiced) or voiced.
The term, however, is used to refer to two separate concepts: Voicing can refer t... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Voice (phonetics)-It can also refer to a classification of speech sounds that tend to be associated with vocal cord vibration but may not actually be voiced at the articulatory level. That is the term's primary use in phonology: to describe phonemes; while in phonetics its primary use is to describe p... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Voice (phonetics)-Yidiny has no underlyingly voiceless consonants, only voiced ones.When used to classify speech sounds, voiced and unvoiced are merely labels used to group phones and phonemes together for the purposes of classification. | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Notation-The International Phonetic Alphabet has distinct letters for many voiceless and voiced pairs of consonants (the obstruents), such as [p b], [t d], [k ɡ], [q ɢ]. In addition, there is a diacritic for voicedness: ⟨◌̬⟩. Diacritics are typically used with letters for prototypically voiceless soun... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Notation-The extensions to the International Phonetic Alphabet have a notation for partial voicing and devoicing as well as for prevoicing: Partial voicing can mean light but continuous voicing, discontinuous voicing, or discontinuities in the degree of voicing. For example, ₍s̬₎ could be an [s] with ... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Notation-Partial voicing can also be indicated in the normal IPA with transcriptions like [ᵇb̥iˑ] and [ædᵈ̥]. | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-The distinction between the articulatory use of voice and the phonological use rests on the distinction between phone (represented between square brackets) and phoneme (represented between slashes). The difference is best illustrated by a rough example.
The English word nods is made up of a... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-However, phonemes are not sounds in themselves. Rather, phonemes are, in a sense, converted to phones before being spoken. The /z/ phoneme, for instance, can actually be pronounced as either the [s] phone or the [z] phone since /z/ is frequently devoiced, even in fluent speech, especially a... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-What complicates the matter is that for English, consonant phonemes are classified as either voiced or voiceless even though it is not the primary distinctive feature between them. Still, the classification is used as a stand-in for phonological processes, such as vowel lengthening that occ... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-English has four pairs of fricative phonemes that can be divided into a table by place of articulation and voicing. The voiced fricatives can readily be felt to have voicing throughout the duration of the phone especially when they occur between vowels. | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-However, in the class of consonants called stops, such as /p, t, k, b, d, ɡ/, the contrast is more complicated for English. The "voiced" sounds do not typically feature articulatory voicing throughout the sound. The difference between the unvoiced stop phonemes and the voiced stop phonemes ... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-English voiceless stops are generally aspirated at the beginning of a stressed syllable, and in the same context, their voiced counterparts are voiced only partway through. In more narrow phonetic transcription, the voiced symbols are maybe used only to represent the presence of articulator... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-When the consonants come at the end of a syllable, however, what distinguishes them is quite different. Voiceless phonemes are typically unaspirated, glottalized and the closure itself may not even be released, making it sometimes difficult to hear the difference between, for example, light... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-In English-Other English sounds, the vowels and sonorants, are normally fully voiced. However, they may be devoiced in certain positions, especially after aspirated consonants, as in coffee, tree, and play in which the voicing is delayed to the extent of missing the sonorant or vowel altogether. | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Degrees of voicing-There are two variables to degrees of voicing: intensity (discussed under phonation), and duration (discussed under voice onset time). When a sound is described as "half voiced" or "partially voiced", it is not always clear whether that means that the voicing is weak (low intensity)... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Degrees of voicing-Juǀʼhoansi and some of its neighboring languages are typologically unusual in having contrastive partially-voiced consonants. They have aspirate and ejective consonants, which are normally incompatible with voicing, in voiceless and voiced pairs. The consonants start out voiced but ... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Voice and tenseness-There are languages with two sets of contrasting obstruents that are labelled /p t k f s x …/ vs. /b d ɡ v z ɣ …/ even though there is no involvement of voice (or voice onset time) in that contrast. That happens, for instance, in several Alemannic German dialects. Because voice is ... | milkshake721/2.1M-wiki-STEM |
Voice (phonetics)-Voice and tenseness-There is a hypothesis that the contrast between fortis and lenis consonants is related to the contrast between voiceless and voiced consonants. That relation is based on sound perception as well as on sound production, where consonant voice, tenseness and length are only different ... | milkshake721/2.1M-wiki-STEM |
Coining (metalworking)-Coining (metalworking)-Coining is a form of precision stamping in which a workpiece is subjected to a sufficiently high stress to induce plastic flow on the surface of the material. A beneficial feature is that in some metals, the plastic flow reduces surface grain size, and work hardens the surf... | milkshake721/2.1M-wiki-STEM |
Coining (metalworking)-Coining (metalworking)-Coining is used to manufacture parts for all industries and is commonly used when high relief or very fine features are required. For example, it is used to produce coins, badges, buttons, precision-energy springs and precision parts with small or polished surface features. | milkshake721/2.1M-wiki-STEM |
Coining (metalworking)-Coining (metalworking)-Coining is a cold working process similar in other respects to forging, which takes place at elevated temperature; it uses a great deal of force to elastically deform a workpiece, so that it conforms to a die. Coining can be done using a gear driven press, a mechanical pres... | milkshake721/2.1M-wiki-STEM |
Coining (metalworking)-Coining in electronic industry-In soldering of electronic components, bumps are formed on bonding pads to enhance adhesion, which are further flattened by the coining process. Unlike typical coining applications, in this case the goal of coining is to create a flat, rather than patterned, surface... | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Tetrahemihexahedron-In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges, and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is (although this is a double cove... | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Tetrahemihexahedron-It is the only non-prismatic uniform polyhedron with an odd number of faces. Its Wythoff symbol is 3/2 3 | 2, but that represents a double covering of the tetrahemihexahedron with eight triangles and six squares, paired and coinciding in space. (It can more intuitively be seen as... | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Tetrahemihexahedron-The "half-as-many" characteristic also means that hemi faces must pass through the center of the polyhedron, where they all intersect each other. Visually, each square is divided into four right triangles, with two visible from each side. | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Related surfaces-It is a non-orientable surface. It is unique as the only uniform polyhedron with an Euler characteristic of 1 and is hence a projective polyhedron, yielding a representation of the real projective plane very similar to the Roman surface. | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Related polyhedra-It has the same vertices and edges as the regular octahedron. It also shares 4 of the 8 triangular faces of the octahedron, but has three additional square faces passing through the centre of the polyhedron.
The dual figure is the tetrahemihexacron.
It is 2-covered by the cuboctahe... | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Related polyhedra-Since the hemipolyhedra have faces passing through the center, the dual figures have corresponding vertices at infinity; properly, on the real projective plane at infinity. In Magnus Wenninger's Dual Models, they are represented with intersecting prisms, each extending in both dire... | milkshake721/2.1M-wiki-STEM |
Tetrahemihexahedron-Related polyhedra-Topologically it is considered to contain seven vertices. The three vertices considered at infinity (the real projective plane at infinity) correspond directionally to the three vertices of the hemi-octahedron, an abstract polyhedron. The other four vertices exist at alternate corn... | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Freudenthal suspension theorem-In mathematics, and specifically in the field of homotopy theory, the Freudenthal suspension theorem is the fundamental result leading to the concept of stabilization of homotopy groups and ultimately to stable homotopy theory. It explains the behavior of si... | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Freudenthal suspension theorem-The theorem is a corollary of the homotopy excision theorem. | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Statement of the theorem-Let X be an n-connected pointed space (a pointed CW-complex or pointed simplicial set). The map X→Ω(ΣX) induces a map πk(X)→πk(Ω(ΣX)) on homotopy groups, where Ω denotes the loop functor and Σ denotes the reduced suspension functor. The suspension theorem then sta... | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Statement of the theorem-A basic result on loop spaces gives the relation πk(Ω(ΣX))≅πk+1(ΣX) so the theorem could otherwise be stated in terms of the map πk(X)→πk+1(ΣX), with the small caveat that in this case one must be careful with the indexing. | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Statement of the theorem-Proof As mentioned above, the Freudenthal suspension theorem follows quickly from homotopy excision; this proof is in terms of the natural map πk(X)→πk+1(ΣX) . If a space X is n -connected, then the pair of spaces (CX,X) is (n+1) -connected, where CX is the ... | milkshake721/2.1M-wiki-STEM |
Freudenthal suspension theorem-Statement of the theorem-Putting this all together, we get πi(X)=πi+1((CX)+,X)=πi+1((ΣX,(CX)−)=πi+1(ΣX) for i+1<2n+2 , i.e. i⩽2n , as claimed above; for i=2n+1 the left and right maps are isomorphisms, regardless of how connected X is, and the middle one is a surjection by excision, ... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Cichoń's diagram-In set theory, Cichoń's diagram or Cichon's diagram is a table of 10 infinite cardinal numbers related to the set theory of the reals displaying the provable relations between these cardinal characteristics of the continuum. All these cardinals are greater than or equal to ℵ1 , the ... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Definitions-Let I be an ideal of a fixed infinite set X, containing all finite subsets of X. We define the following "cardinal coefficients" of I: add min {|A|:A⊆I∧⋃A∉I}.
The "additivity" of I is the smallest number of sets from I whose union is not in I any more. As any ideal is closed under finite un... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Definitions-The "cofinality" of I is the cofinality of the partial order (I, ⊆). It is easy to see that we must have non(I) ≤ cof(I) and cov(I) ≤ cof(I).Furthermore, the "bounding number" or "unboundedness number" b and the "dominating number" d are defined as follows: min {|F|:F⊆NN∧(∀g∈NN)(∃f∈F)(∃∞n... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Diagram-Let B be the σ-ideal of those subsets of the real line that are meager (or "of the first category") in the euclidean topology, and let L be the σ-ideal of those subsets of the real line that are of Lebesgue measure zero. Then the following inequalities hold: Where an arrow from x to y is to... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Diagram-For larger continuum sizes, the situation is less clear. It is consistent with ZFC that all of the Cichoń's diagram cardinals are simultaneously different apart from add (B) and cof (B) (which are equal to other entries), but (as of 2019) it remains open whether all combinations of the card... | milkshake721/2.1M-wiki-STEM |
Cichoń's diagram-Remarks-The British mathematician David Fremlin named the diagram after the Polish mathematician from Wrocław, Jacek Cichoń.The continuum hypothesis, of 2ℵ0 being equal to ℵ1 , would make all of these relations equalities.
Martin's axiom, a weakening of the continuum hypothesis, implies that all card... | milkshake721/2.1M-wiki-STEM |
Mixed receptive-expressive language disorder-Mixed receptive-expressive language disorder-Mixed receptive-expressive language disorder (DSM-IV 315.32) is a communication disorder in which both the receptive and expressive areas of communication may be affected in any degree, from mild to severe. Children with this diso... | milkshake721/2.1M-wiki-STEM |
Mixed receptive-expressive language disorder-Classification-If assessed on the Wechsler Adult Intelligence Scale, for instance, symptoms of mixed receptive-expressive language disorder may show as relatively low scores for Information, Vocabulary and Comprehension (perhaps below the 25th percentile). If a person has di... | milkshake721/2.1M-wiki-STEM |
Mixed receptive-expressive language disorder-Classification-They may also have a more general problem with words or sentences, both comprehension and orally. Some children will have issues with pragmatics – the use of language in social contexts as well; and therefore, will have difficulty with inferring meaning. Furth... | milkshake721/2.1M-wiki-STEM |
Mixed receptive-expressive language disorder-Presentation-Related disorders Studies show that low receptive and expressive language at young ages was correlated to increased autism symptom severity in children in their early school years. Below is a chart depicting language deficits of children on the autistic spectrum... | milkshake721/2.1M-wiki-STEM |
Mixed receptive-expressive language disorder-Management-Children who demonstrate deficiencies early in their speech and language development are at risk for continued speech and language issues throughout later childhood. Similarly, even if these speech and language problems have been resolved, children with early lang... | milkshake721/2.1M-wiki-STEM |
Film recorder-Film recorder-A film recorder is a graphical output device for transferring images to photographic film from a digital source. In a typical film recorder, an image is passed from a host computer to a mechanism to expose film through a variety of methods, historically by direct photography of a high-resolu... | milkshake721/2.1M-wiki-STEM |
Film recorder-Design-Operation All film recorders typically work in the same manner. The image is fed from a host computer as a raster stream over a digital interface. A film recorder exposes film through various mechanisms; flying spot (early recorders); photographing a high resolution video monitor; electron beam rec... | milkshake721/2.1M-wiki-STEM |
Film recorder-Design-For color image recording on a CRT film recorder, the red, green, and blue channels are sequentially displayed on a single gray scale CRT, and exposed to the same piece of film as a multiple exposure through a filter of the appropriate color. This approach yields better resolution and color quality... | milkshake721/2.1M-wiki-STEM |
Film recorder-Design-Formats Film recorders are available for a variety of film types and formats. The 35mm negative film and transparencies are popular because they can be processed by any photo shop. Single-image 4×5 film and 8×10 are often used for high-quality, large format printing.Some models have detachable film... | milkshake721/2.1M-wiki-STEM |
Film recorder-Uses-Film recorders are used in digital printing to generate master negatives for offset and other bulk printing processes. For preview, archiving, and small-volume reproduction, film recorders have been rendered obsolete by modern printers that produce photographic-quality hardcopies directly on plain pa... | milkshake721/2.1M-wiki-STEM |
Film recorder-Uses-Current uses Currently, film recorders are primarily used in the motion picture film-out process for the ever increasing amount of digital intermediate work being done. Although significant advances in large venue video projection alleviates the need to output to film, there remains a deadlock betwee... | milkshake721/2.1M-wiki-STEM |
Film recorder-Key manufacturers-Traditional film recorder manufacturers have all but vanished from the scene or have evolved their product lines to cater to the motion picture industry. Dicomed was one such early provider of digital color film recorders. Polaroid, Management Graphics, Inc, MacDonald-Detwiler, Informat... | milkshake721/2.1M-wiki-STEM |
Film recorder-Key manufacturers-Kodak Lightning I film recorder. One of the first laser recorders. Needed an engineering staff to set up.
Kodak Lightning II film recorder used both gas and diode laser to record on to film.
The last LVT machines produced by Kodak / Durst-Dice stopped production in 2002. There are no LVT... | milkshake721/2.1M-wiki-STEM |
Film recorder-Key manufacturers-Cinevator was made by Cinevation AS, in Drammen, Norway. The Cinevator was a real-time digital film recorder. It could record IN, IP and prints with and without sound Oxberry produced the Model 3100 film recorder camera system, with interchangeable pin-registered movements (shuttles) for... | milkshake721/2.1M-wiki-STEM |
Film recorder-History-Before video tape recorders or VTRs were invented, TV shows were either broadcast live or recorded to film for later showing, using the Kinescope process. In 1967, CBS Laboratories introduced the Electronic Video Recording format, which used video and telecined-to-video film sources, which were th... | milkshake721/2.1M-wiki-STEM |
Film recorder-History-All types of CRT recorders were (and still are) used for film recording. Some early examples used for computer-output recording were the 1954 IBM 740 CRT Recorder, and the 1962 Stromberg-Carlson SC-4020, the latter using a Charactron CRT for text and vector graphic output to either 16mm motion pic... | milkshake721/2.1M-wiki-STEM |
Film recorder-History-In 1988, companies in the United States collectively produced 715 million slides at a cost of $8.3 billion. | milkshake721/2.1M-wiki-STEM |
Film recorder-History-Awards The Academy of Motion Picture Arts and Sciences awarded an Oscar to the makers of the Arrilaser film recorder. The Award of Merit Oscar from the Academy Scientific and Technical Award ceremony was given on 11 February 2012 to Franz Kraus, Johannes Steurer and Wolfgang Riedel. Steurer was aw... | milkshake721/2.1M-wiki-STEM |
First principle-First principle-In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuanced versions of first principles are refer... | milkshake721/2.1M-wiki-STEM |
First principle-In formal logic-In a formal logical system, that is, a set of propositions that are consistent with one another, it is possible that some of the statements can be deduced from other statements. For example, in the syllogism, "All men are mortal; Socrates is a man; Socrates is mortal" the last claim can ... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-In philosophy "first principles" are from first cause attitudes commonly referred to as a priori terms and arguments, which are contrasted to a posteriori terms, reasoning or arguments, in that the former is simply assumed and exist prior to the reasoning process and the latter are deduced or... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-In philosophy "first principles" are often somewhat synonymous with a priori, datum and axiomatic reasoning. | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-Ancient Greek philosophy In Ancient Greek philosophy, a first principle from which other principles are derived is called an arche and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", "authorities" The concept of an arche ... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-Mythical cosmogonies The heritage of Greek mythology already embodied the desire to articulate reality as a whole and this universalizing impulse was fundamental for the first projects of speculative theorizing. It appears that the order of "being" was first imaginatively visualized before it... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-Ionian school The earliest Pre-Socratic philosophers, the Ionian material monists, sought to explain all of nature (physis) in terms of one unifying arche. Among the material monists were the three Milesian philosophers: Thales, who believed that everything was composed of water; Anaximander,... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-Aristotle Terence Irwin writes: When Aristotle explains in general terms what he tries to do in his philosophical works, he says he is looking for "first principles" (or "origins"; archai): In every systematic inquiry (methodos) where there are first principles, or causes, or elements, knowle... | milkshake721/2.1M-wiki-STEM |
First principle-Philosophy-Modern philosophy Descartes Profoundly influenced by Euclid, Descartes was a rationalist who invented the foundationalist system of philosophy. He used the method of doubt, now called Cartesian doubt, to systematically doubt everything he could possibly doubt until he was left with what he sa... | milkshake721/2.1M-wiki-STEM |
First principle-In physics-In physics, a calculation is said to be from first principles, or ab initio, if it starts directly at the level of established laws of physics and does not make assumptions such as empirical model and fitting parameters.
For example, calculation of electronic structure using Schrödinger's equ... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Barnes G-function-In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written ... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Functional equation and integer arguments-The Barnes G-function satisfies the functional equation G(z+1)=Γ(z)G(z) with normalisation G(1) = 1. Note the similarity between the functional equation of the Barnes G-function and that of the Euler gamma function: Γ(z+1)=zΓ(z). | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Functional equation and integer arguments-The functional equation implies that G takes the following values at integer arguments: if if n=1,2,… (in particular, G(0)=0,G(1)=1 and thus G(n)=(Γ(n))n−1K(n) where Γ(x) denotes the gamma function and K denotes the K-function. The functional equation uniq... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Characterisation-Similar to the Bohr-Mollerup theorem for the gamma function, for a constant c>0 , we have for f(x)=cG(x) f(x+1)=Γ(x)f(x) and for x>0 f(x+n)∼Γ(x)nn(x2)f(n) as n→∞ | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Value at 1/2-24 24 e18π−14A−32, where A is the Glaisher–Kinkelin constant. | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Reflection formula 1.0-The difference equation for the G-function, in conjunction with the functional equation for the gamma function, can be used to obtain the following reflection formula for the Barnes G-function (originally proved by Hermann Kinkelin): log log log cot πxdx. | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Reflection formula 1.0-The logtangent integral on the right-hand side can be evaluated in terms of the Clausen function (of order 2), as is shown below: log log sin Cl 2(2πz) The proof of this result hinges on the following evaluation of the cotangent integral: introducing the notation Lc (z) for t... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Reflection formula 1.0-Performing the integral substitution y=2πx⇒dx=dy/(2π) gives log sin log sin y2)dy.
The Clausen function – of second order – has the integral representation Cl log sin x2|dx.
However, within the interval 0<θ<2π , the absolute value sign within the integrand can be omitted, si... | milkshake721/2.1M-wiki-STEM |
Barnes G-function-Reflection formula 2.0-Replacing z with (1/2) − z'' in the previous reflection formula gives, after some simplification, the equivalent formula shown below (involving Bernoulli polynomials): log log log log tan πxdx | milkshake721/2.1M-wiki-STEM |
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